Jump boundary-value problem on a contour with elongate singularities

Abstract

© 2017, Allerton Press, Inc.Let Γ be image of interval (0, 1) under one-to-one continuous mapping φ: (0, 1) → C. If closure of Γ differs from the set Γ bymore than two points, then we call Γ the contour with elongate singularities. We study boundary-value jump problems for analytical functions on that contours, and obtain new criteria for their solvability.